1. Field of the Invention
This invention relates to musical training aids in general and more particularly to devices for determining pitch or perceived frequency of signals generated by musical instruments or human voices.
2. Description of the Prior Art
Various machines that indicate the pitch produced by a musical instrument have been of interest for considerable time. Patents for such devices date from at least 1933. Early devices used mechanical means such as vibrating reeds to make the measurement or displayed the results of the measurement by means such as electrical meter movements. Later inventors turned to electronic equivalents of these mechanical devices. But a multiplicity of tuned filters or quartz reference crystals has the same problems of a multiplicity of vibrating reeds; i.e. precision elements are expensive and multiples of precision elements are multiply expensive. Electrical meter movements have been replaced, for example, by oscilloscopes which have the same limitation; i.e. while being able to display pitches over a single octave range (a 2X change in frequency) with fair accuracy, they cannot display large ranges having a plurality of octaves. A display that will cover the range of two octaves below Middle C to two octaves above Middle C must handle a 16X range of frequencies.
A detailed discussion of the limitations of various technologies previously used in pitch measuring and display systems would imply that their respective corresponding underlying assumptions are correct, but they usually are not. Previous inventors of pitch measuring devices often have not understood the full scope of the problems that they were trying to solve. They therefore generally developed equipment which could not achieve the desired results. The most common errors made by them are listed below with a more detailed discussion following thereafter:
(a) Failure to recognize that the perception of musical pitch is a logarithmic phenomenon, not a linear one. Thus, the attendant display must be one which is intrinsically logarithmic. PA1 (b) Failure to recognize that the perception of musical pitch involves automatic switching between direct frequency and carrier frequency operations. Any equipment that might supplant the human ear must be equally flexible. PA1 (c) Failure to recognize that the production of a precise musical pitch is sufficiently difficult so that any equipment that attempts to assist the effort should be made to be extremely simple to operate and use.
Concerning the perception of musical pitch as a logarithmic operation, the following discussion is pertinent. Middle C is the musician's term for a pitch having a frequency of 256 Hz. The next higher C is at a frequency of 512 Hz while the yet next higher C has a frequency of 1024 Hz. It is to be noted that an error of 5 Hz is a 2.0% error at Middle C, but represents 1.0% error at the C an octave up and a 0.5% error at 1025 Hz. Thus, beat frequency display devices do not represent an optimum nor even a totally useful approach. It is difficult for a trained singer to sing with an accuracy in pitch of better than 2%. Furthermore it is difficult to hear beats much higher than 5 Hz, particularly while concentrating on singing a correct pitch. Thus, hearing a beat frequency for a 2% error at Middle C is difficult, but hearing the 5 Hz error at the C above Middle requires singing at a pitch accurate to 1%, which is effectively impossible, even for the trained singer. The beat frequency approach has no practical utility at all at two octaves above Middle C because the human being is not capable of singing at pitch accuracies of 0.5%.
Electrical meter movements have problems with logarithmic operation or application. A common frequency measuring technique is to generate a voltage linearly proportional to the received frequency and apply this voltage across a meter movement. If 1024 Hz is equivalent to 1.0 volts, 512 Hz would be 0.5 volts and 256 Hz would be 0.25 volts. A meter reading 1.0 volts full scale, and swinging a total of 100 mechanical degrees, would spend half of its swing covering the top sung octave, while the lower octave would occupy only 25%, or 25 degrees, of the swing range. While it might be possible to spot a 2% error at the highest note, which would correspond to 2 degree swing, it would be extremely difficult to perceive a 2% error at the position of the lowest note since the corresponding amount of motion is only 1/2 degree. Techniques for zero supression can be used to improve this readability problem with the obvious drawback that range capability is lost. No one has yet demonstrated the thought of doing a logarithmic conversion of the generated voltage before applying it to the meter movement. In that instance, 1024 Hz could be 1.0 volts and 512 Hz would be 0.5 volts, 526 Hz would be 0.0 volts. In that instance, percentage errors would be evenly distributed over the range of meter motion.
Next, the Carrier Frequency Operation is herein examined. The human voice at high frequencies vibrates in a fashion similar to the vibration of a stringed instrument or a tight rubber band. Corresponding electrical signals are easy to decode by resonant reed or multiple tuned circuits machines. The mathematical expression describing the signal is:
______________________________________ S = A sine 2.pi.ft S is signal strength A is some amplitude .pi. is 3.1416 f is frequency t is time ______________________________________
At low frequencies, however, chest cavity resonances amplitude modulate the vibrations of the vocal chords. A mathematical expression demonstrating the effect of this amplitude-modulated carrier frequency is: EQU S= A (sine 2.pi.f.sub.1 t )X(sine 2.pi.f.sub.2 t)
where f.sub.1 is the frequency of vibration of the vocal chords, which serves as the carrier frequency, and f.sub.2 is the amplitude-modulating information frequency. Human pitch perception will always respond to the lower of these two frequencies. Multiple tuned circuits will respond to the mathematically equivalent signal of: EQU S= A/2 (cosine 2.pi. (f.sub.1 + f.sub.2)t- cosine 2.pi.(f.sub.1 - f.sub.2)t )
thereby indicating the sum and the difference of the frequencies, neither of which may be anywhere near the correct frequency. It would be possible to build a computer-controlled pitch detector which would compute the lower of the two frequencies when sum-and-difference frequencies are present. But there are more than just two frequencies in the human voice or in any instrument such as a trombone or trumpet. Thus, multiple tuned filter systems only have limited usefulness.
Finally, one must look at ease of operation. The ease with which a machine should operate cannot be determined without consideration of the skills and interests of the final user. A musician is trained to think in terms of musical notes and in correcting deviations from those precise notes whenever he is sharp or flat. While he may know that the A above Middle C has a frequency of 440 Hz, he cannot reasonably be expected to know the frequency of any other note or notes, particularly in rapid succession. While his knowledge of frequency is generally very limited, his knowledge of periods is probably non-existent; and that a frequency of 440 Hz corresponds to a period of 2.27 milliseconds is normally beyond his realm of experience. Thus, oscilloscope displays of the periods of signals, while interesting to a person skilled in electronics, are useless to a musician. As another example, a ring of lamps that flash in a clockwise or counter-clockwise fashion when a tone is sharp or flat requires the musician to think in terms of right or left rotation. Since this is foreign to his training and a sharp and a flat more generally correspond to a high and a low, or an up and a down, a single sharp indicator located above a single flat indicator is a more natural arrangement and would be more useful over the rotating ring approach.
The circumstances in which a pitch-measuring instrument might be used should also be considered. If one imagines the musician to be reading some sheet music while playing an instrument or singing, and using the pitch measuring instrument to tell him how he is doing, one must understand that his concentration is on the music. The pitch-measuring instrument should not disturb this concentration any more than necessary. Thus, to require him to sweep his eyes across an electrical meter movement to see where the needle is pointing, and then to ask him to decide for himself how far off the mark the needle may be before his redition is unacceptable, is requiring too much of a performing musician. The pitch readout should be in one place, so its position is known. Beside displaying the basic note, the ideal pitch-measuring instrument should indicate sharp or flat only when the musician is sufficiently far off so that something needs to be done to assist him in returning to an acceptable threshold of pitch deviation. Applicants apparatus will make provision for these requirements.